2023-206

 

Imagine a Cayley Tree, constructed starting from a central node, where each node has degree $k$, except the nodes at distance P from the central node, that have degree one, as shown in the figure above. Considering that the number of nodes reachable in $t\ge 1$ steps from the central node is $k(k-1{)}^{t-1}$, and the number of links is $L=N-1$, where $N$ is the number of nodes, what is the probability of conexion between nodes for $k=4$ and $P=4$?

1. 1/161
2. 2/161
3. 1/41
4. 2/41
5. None of above

Original idea by: Germán Darío Buitrago Salazar